4(3x+8)-9=2x(6x-8)+39

Solution for 4(3x+8)-9=2x(6x-8)+39 equation:

4(3x+8)-9=2x(6x-8)+39

We move all terms to the left:

4(3x+8)-9-(2x(6x-8)+39)=0

We multiply parentheses

12x-(2x(6x-8)+39)+32-9=0


We calculate terms in parentheses: -(2x(6x-8)+39), so:

2x(6x-8)+39

We multiply parentheses

12x^2-16x+39

Back to the equation:

-(12x^2-16x+39)


We add all the numbers together, and all the variables

12x-(12x^2-16x+39)+23=0

We get rid of parentheses

-12x^2+12x+16x-39+23=0

We add all the numbers together, and all the variables

-12x^2+28x-16=0

a = -12; b = 28; c = -16;
Δ = b2-4ac
Δ = 282-4·(-12)·(-16)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4}{2*-12}=\frac{-32}{-24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4}{2*-12}=\frac{-24}{-24}
=1
$